>>4459573f/8 is talking about aperture. Aperture is one of the defining characteristics of a lens. Narrower apertures are higher numbers f/11, f/16 etc. and wider apertures are lower f/4, f/2 etc.
The notation we're using is the focal length of the lens (say a 50mm lens) divide by the aperture diameter (say 25mm) which makes an f/2 lens. If you grabbed a 100mm lens, a 25mm aperture would no longer be f/2, it would be f/4. This is important because wider aperture lenses involve more glass, bigger lenses, and higher price. But, using wider apertures gathers more light.
If you can gather an additional stop of light (going from f/5.6 to f/4) you now have twice as much light gathered than before. So to get a properly exposed image, you can now lower your ISO by a whole stop, or raise your shutter speed by a whole stop. Going from ISO 6400 to 3200 might be the difference between an unusably noisy image, or going from 1/60th shutter speed to 1/125th might be the difference between motion blur fucking your shot or not.
You can always stop down an aperture (except in very specific lenses) to go narrower, but you can't go wider than what's marked on the barrel. So we circle back to wider aperture lenses beng prefererd, IF you need the extra light, which it sounds like for your use case you do.
Photographing things at night that are moving requires: High shutter speed (to freeze the motion instead of getting a blurry mess), and a low enough ISO to not get a noisy shitty blob instead of clean sharp details. You can buy a newer, bigger sensor camera to help with the ISO problem, but even modern full frame cameras still need at least a moderately wide aperture lens to avoid cranking the ISO too high.
>there really should be a FAQThere's a link stickied up top that's an entire page of basic information
But I do agree an infographic or something might be useful to sticky to the catalog.